Integration is (fundamentally) summation

Calculus Level 5

If \(\displaystyle \large \int _{ 0 }^{ 1 }{ { x }^{ 2015 }{ e }^{ -x }dx } =2015!-k\sum _{ r=0 }^{ 2015 }{ \left( ^{ 2015 }{ { C }_{ r } }\times \left( r! \right) \right) } \), find \(\left\lfloor 100k \right\rfloor \).

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